Question

f(x)=sin ( 2x + pi/3 )
1)a) préciser la peridoe de f
b) montrer que delta : x = 7pi/12 est un awe de symétrie de Cf
c) on déduire un domaine d'étude de f
2) etudier les variations de f et tracer la courbe dans un repere orthnormé
3) soit g(x)=f(x-pi/2)
Tracer Cg a partir de Cf
#Michele_Laino @Michele_Laino

Answer 1

By definition of a period T of a periodic function f, we have:
f(x+T)=f(x)
Now, applying that condition to our function, we get:
\[\sin \left( {2\left( {x + T} \right) + \frac{\pi }{3}} \right) = \sin \left( {2x + \frac{\pi }{3}} \right)\]
Developing the necessary computation, we get the subsequent condition:
\[\Large \cos \left( {2T} \right) = 1\], please check that formula.
So what is T?

Answer 2

f (x) = sin (2x + pi / 3)
1) a) specify the reporting period of f
b) show that delta x = 7ft / 12 is an axe symmetry Cf
c) deriving a field of study of f
2) study the variations of f and graph it in a repere orthnormé
3) be g (x) = f (x-pi / 2)
Tracer Cg from Cf

Answer 3

the above quantity T, answers to question a)

Answer 4

yes thank you

Answer 5

please, what is Cf?

Answer 6

la courbe de f

Answer 7

the graph of f(x)

Answer 8

yes

Answer 9

let's suppose that x=a, is a symmetry axis, then we can write:
f(x)=f(2a-x)
substituting our function, we get:
\[\Large \sin \left( {2x + \frac{\pi }{3}} \right) = \sin \left( {2\left( {2a - x} \right) + \frac{\pi }{3}} \right)\]
then, starting from that condition, what value do you get for a?

Answer 10

7pi/12

Answer 11

are you sure?

Answer 12

when we have the subsequent equality:
sin x = sin y

Answer 13

do you know that answer?

Answer 14

no xD to be honest i never passed math exam this year

Answer 15

the answer is:
when the subsequent condition holds:
x= pi- y

Answer 16

\[\Large x = \pi - y\]

Answer 17

so we have to solve this equation for a:
\[\Large 2x + \frac{\pi }{3} = \pi - \left\{ {2\left( {2a - x} \right) + \frac{\pi }{3}} \right\}\]
what is a?

Answer 18

what is a ? the professor said x= 7pi/12

Answer 19

There I keep in mind the subsequent drawing: